International Journal of Mathematics and Mathematical Sciences 
Volume 2006 (2006), Article ID 46930, 5 pages
doi:10.1155/IJMMS/2006/46930

Measure of noncompactness of operators and matrices on the spaces c and c0

Bruno De Malafosse,1 Eberhard Malkowsky,2 and Vladimir Rakočević3

 1LMAH Université du Havre, IUT du Havre, BP 4006, Le Havre 76610, France
2Mathematisches Institut, Universität Giessen, Arndtstrasse 6, Giessen D-35392, Germany
3Department of Mathematics, Faculty of Sciences and Mathematics, University of Niš, Višegradska 33, Niš 18000, Serbia and Montenegro
Received 16 September 2005; Revised 11 December 2005; Accepted 4 January 2006

Abstract

In this note, using the Hausdorff measure of noncompactness, necessary and sufficient conditions are formulated for a linear operator and matrices between the spaces c and c0 to be compact. Among other things, some results of Cohen and Dunford are recovered.